• 제목/요약/키워드: Dirichlet boundary conditions positivity preserving flow

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A SIMPLE CHARACTERIZATION OF POSITIVITY PRESERVING SEMI-LINEAR PARABOLIC SYSTEMS

  • Haraux, Alain
    • 대한수학회지
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    • 제54권6호
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    • pp.1817-1828
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    • 2017
  • We give a simple and direct proof of the characterization of positivity preserving semi-flows for ordinary differential systems. The same method provides an abstract result on a class of evolution systems containing reaction-diffusion systems in a bounded domain of ${\mathbb{R}}^n$ with either Neumann or Dirichlet homogeneous boundary conditions. The conditions are exactly the same with or without diffusion. A similar approach gives the optimal result for invariant rectangles in the case of Neumann conditions.